The theoretical problems related to the stability of reflection transformations and the convergence of the conjugate gradient method have been studied in [4, 6] (in the case of the above method of parallel calculation it is not necessary to study them additionally).
Let us note that the effectiveness of parallel calculations depends on both the algorithm under consideration and the MECM architecture. Thus in the case of the reflection method, the Ke will be determined by two factors, i.e. (firstly) by the difficulty of using the matrix symmetry, and (secondly) by the nonuniform utilization of the processors. With such an organization of the calculations, it is possible to increase the overall effectiveness of MECM by either letting the newly available processors of a new problem operate in the multiprocessor mode, or by improving the coefficient of uniform partition of the original information. For the conjugate gradient method the effectiveness factor is fairly high. This conclusion evidently holds for many well-known iteration methods when the original data of the problem are assigned in the way described above.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
V. M. Glushkov, Yu. V. Kapitonova, A. A. Letichevskii, and S. P. Gorlach, “Macroconveyer calculations of functions over data arrays,” Kibernetika, No. 4, 13–21 (1981).
A. H. Sameh and A. Kuck, “A parallel QR-algorithm for symmetric tridiagonal matrices,” IEEE Trans. Comput.,26, No. 2, 32–41 (1977).
A. H. Sameh, “On Jacobi and Jacobi-like algorithms for a parallel computer,” Math. Comput.,2, No. 25, 579–590 (1971).
J. H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford (1965).
W. W. Bradbury and R. Fletcher, “New iterative methods for solution of the eigenproblem,” Numer. Math.,2, No. 9, 260–267 (1966).
G. V. Savinov, “A generalized method of conjugate gradients for finding the eigenvalues,” Tr. LKI, No. 120, 55–58 (1977).
Translated from Kibernetika, No. 6, pp. 39–44, November–December, 1983.
About this article
Cite this article
Molchanov, I.N., Khimich, A.N. Some algorithms for the solution of the symmetric eigenvalue problem on a multiprocessor electronic computer. Cybern Syst Anal 19, 779–783 (1983). https://doi.org/10.1007/BF01068566
- Operating System
- Artificial Intelligence
- System Theory
- Original Data